Viewing a single comment thread. View all comments

aaeme t1_j0fcos6 wrote

Reply to comment by nsjr in Does rotation break relativity? by starfyredragon

>Can we consider that Earth is "accelerating"/spinning referent to the sun, because it's rotating around the sun? And the sun around the galaxy? And the galaxy around some center of mass of local group?

Absolutely we can and should but with a big caveat: general relativity tells us that the earth, the sun, the galaxy and everything that is only 'moving' due to gravity is following geodesics: 'straight' lines in a curved spacetime; they're not accelerating relative to spacetime; they're weightless in free fall. Just like a 'stationary' object infinitely far from any gravitational effects.

Nevertheless, things are definitely in motion. There is no frame of reference where everything is still. The earth is definitely rotating around the sun (and the sun around the galaxy) relative to any outside observer. But from the earth's frame of reference we can consider ourselves 'stationary' because we don't experience any acceleration from our orbit.

If we never saw the night sky it would be difficult if not impossible to prove by experiment that the earth is in motion around the sun. We could prove it's spinning at 1 rev per day because that's not due to gravity, the real forces of atoms in the Earth's crust are constantly accelerating us upwards against the freefall flow of spacetime and that allows us to spin at less than orbital speeds and feel the weight of things.

>So calculate the real time/speed of something really far, like another galaxy, can become very tricky

It is tricky to measure distant velocities but not really because of our motion or any acceleration: accelerations are rarely big enough to make massive changes in velocity quickly. There are exceptions: measuring the speed of expansion of a supernova would be difficult because it's accelerating (or decelarating) hard but not so for the motion of a star or galaxy across the sky. The difficulties in measuring that are nothing to do with its acceleration or ours. They are because all velocities are relatively small compared to the enormity of space. They might take a century to move a thousandth of a degree across the sky.

Nevertheless, for really accurate measurements of, say, the velocity of Andromeda relative to the Milky Way, we do have to take into account the movement of the Earth round the Sun and the movement of the Sun around and within the Milky Way but that's pretty easy to do, we know those velocities well and we just subtract them from the raw measurements.

I hope all that makes sense and I haven't laboured the point.

18

pelican_chorus t1_j0gmcvb wrote

>If we never saw the night sky it would be difficult if not impossible to prove by experiment that the earth is in motion around the sun.

Am I right in thinking that there is, in fact, no experiment that could tell whether we were moving around the sun, or the sun moving around us (in the same way that a car moving at constant speed towards a wall can say whether it is moving or the wall is moving)?

Spinning, however, seems different, right? We can tell that the Earth is spinning on its own axis using Foucault's Pendulum, right?

1

Game_Minds t1_j0gtonc wrote

Well no. If we had no other ways of determining the mass of the sun, then maybe. But we can do gravitational lensing measurements and things, and the whole eclipse thing, and fusion doesn't happen at earth sized masses, etc etc etc. There are many ways to determine that the sun is millions of times the size of earth, and that the system is spinning, and put both together and we are orbiting the sun

1

aaeme t1_j0h75op wrote

The hypothetical scenario is something like if we always lived in caverns miles beneath the surface so didn't even know the sun existed. Could we tell by local experiments that the earth was in motion and in orbit and the metrics of that orbit?

I think in theory we could from tidal forces and we'd notice a periodicity of a year for those and could in theory work the rest out.

2

pelican_chorus t1_j0ha7gb wrote

But isn't an orbiting body in free-fall? And a body in free-fall can't feel the force of the body it's falling towards, right? That was my point. Isn't it an inertial frame?

1

aaeme t1_j0hb31e wrote

At an infinitesimal point yes but across a volume tidal forces exist. There would be a slight stretching in the direction of the Sun and squeezing tangential to the Sun.

Across a year those forces would rotate 360° and not uniformly (we could calculate the eccentricity of the elliptical orbit from that).

Edit: measuring all that would be a lot more difficult because the earth is spinning so would have to figure that out so we can subtract the effects of that on our measurements.

It's hard to imagine how any species could properly understand physics well enough to do this without seeing the night sky so perhaps a better mind experiment is if a scientist got teleported to a sealed windowless box on a random planet somewhere in the universe could they tell by measurement whether the planet was in orbit around a star or not and the details of that orbit. I'm 99% sure they could from tidal forces and possibly by other means too.

Edit 2: another way to tell would be from the time-dilation differential from one side of the room to the other. A clock slightly deeper in the star's gravity well would run slightly slower.

1